Details

sample33.0ms

Algorithm

intervals

Results

9.0ms	190×	body	80	valid
5.0ms	19×	body	2560	valid
4.0ms	16×	body	1280	valid
3.0ms	10×	body	5120	valid
2.0ms	13×	body	640	valid
1.0ms	4×	body	320	valid
0.0ms	4×	body	160	valid

simplify6.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	22	8
1	24	8
2	24	8

prune3.0ms

Filtered

1 candidates to 0 candidates (0.0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 41.4b

Counts

2 → 1

localize10.0ms

Local error

Found 2 expressions with local error:

1.4b	(+ (sqrt (+ (* re re) (* im im))) re)
30.6b	(sqrt (+ (* re re) (* im im)))

rewrite11.0ms

Algorithm

rewrite-expression-head

Rules

5×	`*-un-lft-identity`
4×	`add-sqr-sqrt` `add-log-exp`
3×	`pow1` `add-cube-cbrt` `sqrt-prod`
2×	`add-exp-log` `flip3-+` `sqrt-div` `add-cbrt-cube` `flip-+`
1×	`+-commutative` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `sum-log` `distribute-lft-out`

Counts

2 → 27

Calls

2 calls:

7.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
4.0ms	(sqrt (+ (* re re) (* im im)))

series87.0ms

Counts

2 → 6

Calls

2 calls:

46.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
41.0ms	(sqrt (+ (* re re) (* im im)))

simplify80.0ms

Algorithm

egg-herbie

Counts

33 → 33

Iterations

Useful iterations: 3 (28.0ms)

Iter	Nodes	Cost
0	141	198
1	358	186
2	866	182
3	2557	181
4	5001	181

prune118.0ms

Filtered

33 candidates to 29 candidates (87.9%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	26	7	33
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	27	7	34

Merged error: 16.9b

Counts

34 → 7

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(* 2.0 (/ (* im im) (- (sqrt (+ (* re re) (* im im))) re)))
4.4b	(sqrt (* 2.0 (/ (* im im) (- (sqrt (+ (* re re) (* im im))) re))))
21.9b	(/ (* im im) (- (sqrt (+ (* re re) (* im im))) re))
30.6b	(sqrt (+ (* re re) (* im im)))

rewrite44.0ms

Algorithm

rewrite-expression-head

Rules

27×	`add-sqr-sqrt`
18×	`add-exp-log` `add-cbrt-cube`
16×	`*-un-lft-identity`
13×	`times-frac`
12×	`associate-r`
10×	`pow1` `add-cube-cbrt`
7×	`sqrt-prod`
6×	`associate-/r*` `difference-of-squares`
5×	`prod-exp` `cbrt-unprod`
4×	`cbrt-undiv` `div-exp` `associate-/r/` `add-log-exp`
3×	`sqrt-pow1` `sqrt-div` `associate-l` `distribute-lft-out--`
2×	`flip3--` `pow1/2` `associate-*r/` `pow-prod-down` `flip--` `div-inv` `unswap-sqr`
1×	`rem-sqrt-square` `frac-2neg` `flip3-+` `clear-num` `-commutative` `flip-+` `associate-/l`

Counts

4 → 89

Calls

4 calls:

13.0ms	(* 2.0 (/ (* im im) (- (sqrt (+ (* re re) (* im im))) re)))
14.0ms	(sqrt (* 2.0 (/ (* im im) (- (sqrt (+ (* re re) (* im im))) re))))
10.0ms	(/ (* im im) (- (sqrt (+ (* re re) (* im im))) re))
4.0ms	(sqrt (+ (* re re) (* im im)))

series424.0ms

Counts

4 → 12

Calls

4 calls:

86.0ms	(* 2.0 (/ (* im im) (- (sqrt (+ (* re re) (* im im))) re)))
220.0ms	(sqrt (* 2.0 (/ (* im im) (- (sqrt (+ (* re re) (* im im))) re))))
81.0ms	(/ (* im im) (- (sqrt (+ (* re re) (* im im))) re))
37.0ms	(sqrt (+ (* re re) (* im im)))

simplify55.0ms

Algorithm

egg-herbie

Counts

101 → 101

Iterations

Useful iterations: 2 (45.0ms)

Iter	Nodes	Cost
0	449	927
1	1985	795
2	5001	792

prune244.0ms

Filtered

101 candidates to 75 candidates (74.3%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	95	6	101
Fresh	5	1	6
Picked	1	0	1
Done	0	0	0
Total	101	7	108

Merged error: 12.8b

Counts

108 → 7

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (- (sqrt (+ (* re re) (* im im))) re) im)
0.1b	(/ im (/ (- (sqrt (+ (* re re) (* im im))) re) im))
4.4b	(sqrt (* 2.0 (/ im (/ (- (sqrt (+ (* re re) (* im im))) re) im))))
30.6b	(sqrt (+ (* re re) (* im im)))

rewrite48.0ms

Algorithm

rewrite-expression-head

Rules

156×	`times-frac`
144×	`add-sqr-sqrt`
111×	`*-un-lft-identity`
79×	`add-cube-cbrt`
32×	`difference-of-squares`
25×	`associate-/r*`
20×	`sqrt-prod`
16×	`distribute-lft-out--`
11×	`add-exp-log` `add-cbrt-cube`
9×	`associate-/l*`
8×	`pow1`
6×	`div-inv`
4×	`cbrt-undiv` `div-exp` `add-log-exp`
3×	`sqrt-pow1` `sqrt-div`
2×	`frac-2neg` `pow1/2` `clear-num` `associate-/l/`
1×	`rem-sqrt-square` `flip3--` `flip3-+` `div-sub` `associate-*r/` `pow-prod-down` `associate-/r/` `flip--` `flip-+`

Counts

4 → 175

Calls

4 calls:

9.0ms	(/ (- (sqrt (+ (* re re) (* im im))) re) im)
11.0ms	(/ im (/ (- (sqrt (+ (* re re) (* im im))) re) im))
12.0ms	(sqrt (* 2.0 (/ im (/ (- (sqrt (+ (* re re) (* im im))) re) im))))
4.0ms	(sqrt (+ (* re re) (* im im)))

series399.0ms

Counts

4 → 12

Calls

4 calls:

80.0ms	(/ (- (sqrt (+ (* re re) (* im im))) re) im)
79.0ms	(/ im (/ (- (sqrt (+ (* re re) (* im im))) re) im))
203.0ms	(sqrt (* 2.0 (/ im (/ (- (sqrt (+ (* re re) (* im im))) re) im))))
37.0ms	(sqrt (+ (* re re) (* im im)))

simplify93.0ms

Algorithm

egg-herbie

Counts

187 → 187

Iterations

Useful iterations: 2 (71.0ms)

Iter	Nodes	Cost
0	667	2309
1	3226	2168
2	5001	2159

prune411.0ms

Filtered

187 candidates to 124 candidates (66.3%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	183	4	187
Fresh	3	3	6
Picked	0	1	1
Done	0	0	0
Total	186	8	194

Merged error: 9.7b

Counts

194 → 8

localize16.0ms

Local error

Found 4 expressions with local error:

1.8b	(log (sqrt (* 2.0 (/ im (/ (- (sqrt (+ (* re re) (* im im))) re) im)))))
3.6b	(exp (log (sqrt (* 2.0 (/ im (/ (- (sqrt (+ (* re re) (* im im))) re) im))))))
4.4b	(sqrt (* 2.0 (/ im (/ (- (sqrt (+ (* re re) (* im im))) re) im))))
30.6b	(sqrt (+ (* re re) (* im im)))

rewrite51.0ms

Algorithm

rewrite-expression-head

Rules

16×	`pow1`
9×	`add-sqr-sqrt`
8×	`add-cube-cbrt` `log-prod` `*-un-lft-identity` `log-pow`
7×	`exp-prod` `sqrt-pow1`
6×	`sqrt-prod`
5×	`add-exp-log` `sqrt-div`
4×	`pow1/2` `exp-sum` `add-cbrt-cube` `add-log-exp`
3×	`associate-*r/` `pow-prod-down`
2×	`log-div`
1×	`rem-sqrt-square` `flip3-+` `exp-diff` `rem-log-exp` `flip-+` `rem-exp-log`

Counts

4 → 64

Calls

4 calls:

13.0ms	(log (sqrt (* 2.0 (/ im (/ (- (sqrt (+ (* re re) (* im im))) re) im)))))
15.0ms	(exp (log (sqrt (* 2.0 (/ im (/ (- (sqrt (+ (* re re) (* im im))) re) im))))))
13.0ms	(sqrt (* 2.0 (/ im (/ (- (sqrt (+ (* re re) (* im im))) re) im))))
8.0ms	(sqrt (+ (* re re) (* im im)))

series769.0ms

Counts

4 → 12

Calls

4 calls:

317.0ms	(log (sqrt (* 2.0 (/ im (/ (- (sqrt (+ (* re re) (* im im))) re) im)))))
202.0ms	(exp (log (sqrt (* 2.0 (/ im (/ (- (sqrt (+ (* re re) (* im im))) re) im))))))
212.0ms	(sqrt (* 2.0 (/ im (/ (- (sqrt (+ (* re re) (* im im))) re) im))))
37.0ms	(sqrt (+ (* re re) (* im im)))

simplify117.0ms

Algorithm

egg-herbie

Counts

76 → 76

Iterations

Useful iterations: 3 (108.0ms)

Iter	Nodes	Cost
0	333	788
1	1070	711
2	4152	667
3	5001	660

prune200.0ms

Filtered

76 candidates to 58 candidates (76.3%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	76	0	76
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	76	8	84

Merged error: 9.7b

Counts

84 → 8

regimes163.0ms

Accuracy

51.6% (13.7b remaining)

Error of 25.5b against oracle of 11.8b and baseline of 40.1b

bsearch95.0ms

Steps

Iters	Range		Point
8	4.570696158225727e-52	1.1612467142622228e-47	1.7249368426738814e-51
7	-1.551713512972122e+88	-3.787686207962144e+86	-8.400557775792221e+86

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	45	22
1	45	22

end0.0ms

sample898.0ms

Algorithm

intervals

Results

286.0ms	6036×	body	80	valid
187.0ms	672×	body	2560	valid
111.0ms	488×	body	1280	valid
93.0ms	276×	body	5120	valid
52.0ms	298×	body	640	valid
22.0ms	157×	body	320	valid
7.0ms	73×	body	160	valid

Details

sample33.0ms

simplify6.0ms

prune3.0ms

localize10.0ms

rewrite11.0ms

series87.0ms

simplify80.0ms

prune118.0ms

localize11.0ms

rewrite44.0ms

series424.0ms

simplify55.0ms

prune244.0ms

localize13.0ms

rewrite48.0ms

series399.0ms

simplify93.0ms

prune411.0ms

localize16.0ms

rewrite51.0ms

series769.0ms

simplify117.0ms

prune200.0ms

regimes163.0ms

bsearch95.0ms

simplify2.0ms

end0.0ms

sample898.0ms

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